Title: Spin representations of maximal compact subgroups/subalgebras of real Kac-Moody groups/algebras Abstract: String theorists are interested in the maximal compact subgroup/subalgebra of the split real Kac-Moody group/algebra of type E10. Damour et al. and Nicolai et al. described a spin representation of this Lie algebra as an extension of the classical spin representation of the so(10) embedded along the A9 subdiagram. In my talk I will discuss how to construct such a spin representation for arbitrary simply laced type. The quotients thus obtained will always be compact and even perfect if the diagram does not admit any isolated nodes. Furthermore I will show how to lift this representation to group level via amalgamation methods. Along the way we will construct a double spin cover of the maximal compact subgroup of the simply laced real Kac-Moody group whose existence has been conjectured by string theorists. Moreover, using covering theory of compact Lie groups, this in turn will allow us to construct spin covers for arbitary two-spherical real Kac-Moody groups. The observations on algebra level are joint with G. Hainke and P. Levy, those on group level joint with D. Ghatei, M. Horn and S. Weiss.